The figure shows two semicircles. Find the area of the shaded part in terms of pi. Please explain in detail thank you!

  3pi/2

This is equivalent to 1.5pi

The units for the area are in square centimeters.

Work Shown:

The larger semicircle has radius 2 cm.

So r = 2 is plugged into the area of a semicircle formula below

A = (pi*r^2)/2

A = (pi*2^2)/2

A = (4pi)/2

A = 2pi

The area of the larger semicircle is 2pi square cm.

Repeat those steps but now use r = 1. This will compute the area of the unshaded smaller semicircle

A = (pi*r^2)/2

A = (pi*1^2)/2

A = pi/2

The area of the smaller unshaded semicircle is pi/2 square cm.

From here, we subtract the two results to get the shaded area:

(larger semicircle area) - (smaller semicircle area) = (2pi) - (pi/2) = 3pi/2

This is equivalent to 1.5pi since 3/2 = 1.5

it's